"Max" as in "Claude 3.7 Sonnet MAX" is apparently Cursor-specific marketing - by default they don't use all the context of the model and set the thinking budget

"Max" as in "Claude 3.7 Sonnet MAX" is apparently Cursor-specific marketing - by default they don't use all the context of the model and set the thinking budget to a lower value than the maximum allowed. So essentially it's the exact same 3.7 Sonnet model, just with different settings.